Abstract

We introduce a new class of density estimators, termed look-ahead density estimators, for performance measures associated with a Markov chain. Look-ahead density estimators are given for both transient and steady-state quantities. Look-ahead density estimators converge faster (especially in multi-dimensional problems) and empirically give visually superior results relative to more standard estimators, such as kernel density estimators. Several numerical examples that demonstrate the potential applicability of look-ahead density estimation are given. 1 Introduction Visualization is becoming increasingly popular as a means of enhancing one's understanding of a stochastic system. In particular, rather than just reporting the mean of a distribution, one often finds that more useful conclusions may be drawn by seeing the density of the underlying random variable. We will consider the problem of computing the densities of performance measures associated with a Markov chain. For chains on a ...

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